CONFORMAL PLASMONIC A-SI:H SOLAR CELLS WITH NON-PERIODIC LIGHT TRAPPING PATTERNS

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1 CONFORMAL PLASMONIC A-SI:H SOLAR CELLS WITH NON-PERIODIC LIGHT TRAPPING PATTERNS Vivian E. Ferry 1,2, Marc A. Verschuuren 3, Claire van Lare 2, Ruud E. I. Schropp 4, Albert Polman 2, and Harry A. Atwater 1 1 California Institute of Technology, Pasadena, CA, USA 2 FOM Institute AMOLF, Amsterdam, The Netherlands 3 Philips Research, Eindhoven, The Netherlands 4 Utrecht University, Utrecht, The Netherlands ABSTRACT Light trapping via plasmonic nanostructures has emerged as a novel method for guiding and confining light in nanoscale photovoltaics. In our design, the metal nanostructures are built directly into the back contact of an a-si:h device, such that the large scattering cross section of the plasmonic particles couples incident sunlight into localized and guided modes overlapping with the a-si:h layer. This enables the use of ultrathin absorbing layers, which are attractive for cost and stability as well as higher open circuit voltages. Here we show that electromagnetic simulation can be used to accurately simulate nanopatterned solar cells, including for randomly textured and non-periodic patterns. We also show that non-periodic arrangements of plasmonic nanostructures are promising for enhancing photocurrent in ultrathin film a-si:h solar cells. INTRODUCTION Light trapping is a critical component of many thin film Si solar cells. Commercial devices are typically designed incorporating a randomly textured surface to scatter and trap light within the semiconductor. These rough surfaces can be introduced via either superstrate or substrate-type fabrication, and may consist of textured metal-oxides, glass, plastic, metal, or other materials [1-7]. While much work has been devoted to optimizing these random designs, the texture typically develops from either native deposition or etching. Plasmonic and other nanophotonic designs for solar cells have recently emerged as alternative methods for light trapping, and designs based on nanowires, gratings, photonic crystals, and plasmonic nanostructures have been studied, among others [8-14]. Plasmonic nanostructures possess large resonant scattering cross sections, which may lead to both enhanced local absorption and enhanced coupling to waveguide modes of the device. The local absorption effects due to scattering are dominant in regions of the spectrum where the semiconductor is strongly absorbing and propagation lengths are short, whereas coupling to waveguide modes is more visible in long wavelength regions where absorption is weaker. Considered over the full solar spectrum bandwidth, the arrangement of scatterers is thus critical to achieving a broadband response. We have previously shown that periodic arrangements of metal nanoparticles built into the back contact of an a-si:h solar cell can enhance photocurrent beyond that of a randomly textured reference cell, using Ag-coated Asahi U-type glass as a reference texture [13]. In periodic patterns, the external quantum efficiency (EQE) spectrum exhibits peaks due to the waveguide modes present at each periodicity, which we confirmed using angle-resolved photocurrent mapping. Randomly textured surfaces, in contrast, show a very smooth EQE spectrum without waveguide mode signatures. This paper looks at one example of a different type of pattern: a quasicrystal penrose tiling. This tiling has both short and long range order, but is non-periodic. Electromagnetic simulation has become an essential part of plasmonic solar cell design, allowing for a large variety of nanostructures to be examined before fabrication. Combined with advanced large-area nanopatterning techniques such as nanoimprint lithography, we show here that simulations can very accurately reproduce the photocurrent from measured devices, provided that care is taken to accurately reproduce the geometry of the cells. SIMULATION LAYOUT Figure 1 Schematic of conformal plasmonic a-si:h solar cell with a periodic array of Ag nanoparticles built into the back contact /11/$ IEEE

2 Figure 1 shows a schematic design for the solar cells we consider here. Hemispherical nanoparticles are built into a metallic Ag back contact, then overcoated with a 130 nm thick layer of ZnO:Al. An n-i-p a-si:h solar cell conformally coats the ZnO:Al layer, followed by an 80 nm thick ITO top contact. For the purposes of simulation, differences in the optical constants between the doped regions and the intrinsic region are ignored, and a finger grid on top of the ITO is not included. The simulations are done using the Finite Difference Time Domain (FDTD) method, which numerically solves Maxwell s equations in three dimensions. A refractive index monitor and an electric field monitor are included over the entire simulation volume. The photon flux across the entire simulation volume can be calculated from the divergence of the Poynting vector, which depends on the magnitude of the electric field E and the imaginary part of the permittivity of each material, ε. ε Φ(λ) = E 2 2h By mapping this photon flux against the refractive index, the photon flux in each layer can be separated, and after integrating over volume at each wavelength either the optical generation rate in the semiconductor or the parasitic losses in the other materials can be calculated [14]. Integrating over the solar spectrum gives an appropriate figure of merit for optimization of design. While the technique does not account for device physics of carrier collection, it is a reasonable approximation of photocurrent provided that most of the generated carriers are collected. FDTD simulations rely on accurate modeling of the complex refractive index of each material. For the ITO, ZnO:Al, and a-si:h the optical constants were measured, and approximated as having a constant refractive index at each wavelength point in the simulation (although a different constant at each point). For Ag, literature values for a Lorentz-Drude fit to data were used to account for the dispersion [15]. Since FDTD is a time-domain technique, dispersive materials must be fit to an analytic model to be modeled. When the nanopatterns are periodic, simulation boundary conditions are straightforward. A single unit cell can be simulated rather than a large area, with periodic boundaries applied in the plane, and perfectly matched layers (PML) out of the plane. For patterns without periodicity, such as randomly textured surface or larger area arrangements of nanostructures, periodic boundary conditions are still the most appropriate choice due to the errors inherent to plane wave sources and PML boundaries in the x-y dimensions. With care in choosing the simulation size to have both a sufficiently large size to (1) Figure 2 Solar spectrum weighted cross sections of photon flux in flat (left), periodic (middle), Asahi texture (right). suppress errors from the periodic assumption and a sufficiently small size to be computationally tractable, nonperiodic systems can be simulated with good fidelity. Indeed, the flexibility of FDTD with regard to non-periodic surfaces is one of its primary advantages over other simulation methods: other than the boundary conditions, as the simulation method makes no assumptions about symmetry in the surface. This allows arbitrary simulation profiles such as those obtained from AFM data or SEM images to be computed directly, with calculation of both the local effects and the resulting guided modes. IMAGING PHOTON FLUX Since the absorption is calculated over the entire volume, this technique can also be used to construct images of the photon flux (or generation rate in the semiconductor) within the cell. These images can also be weighted by the solar spectrum before integrating over the volume, giving an aggregate picture of the absorption in the solar cell for different light trapping nanostructures. Figure 2 shows cross sections of the weighted photon flux in three different light trapping surfaces in a cell with 115 nm i-layer thickness. On the left is a flat cell, where all absorption in the a-si:h layer is due to Fabry-Perot resonances in the thin film caused by the coherent interference of light from multiple reflections off each interface. Weighting by the solar spectrum results in slightly higher absorption in some locations than others due to these Fabry-Perot resonances. In the middle image, a cell with a periodic array of 500 nm pitch between Ag nanoparticles is shown, where the conformal broadening from each layer deposition is accounted for. The overall absorption in the a-si:h is clearly higher than in the flat film, and is slightly higher in the region over the scatterer and weaker between the particles. The image on the right is from an Ag-coated Asahi U-type texture, where the AFM profile of the Ag-coated surface was fed directly into the simulation. Local inhomogeneities are present within the a-si:h layer. In all three cases, it is clear that the strongest absorption is in the photocurrent-generating a- Si:H region, that ITO is a significant source of parasitic absorption, and that the ZnO:Al is relatively low-loss. SIMULATING RANDOM TEXTURES /11/$ IEEE

3 depends more strongly on the top of the surface than back and this surface is less accurately depicted. The photocurrent on the blue side of the spectrum will also be more strongly affected by defects at the p/i interface, internal fields, and carrier transport, none of which are captured by the FDTD simulations. Nevertheless, the agreement between experiment and simulation is good. Figure 3 AFM scan of Ag-coated Asahi U-type texture, as used in simulation. The error from the smaller sampled AFM region can be estimated using a statistical bootstrapping method. One option is to run simulations of the same size with other 2 µm x 2 µm regions of the surface and compare the simulated curves, but this is a computationally intensive solution. A second option is to use subsampling over a single simulation to estimate the standard deviation. For these Asahi substrates, the standard deviation for the generation rate in the a-si:h was estimated below 3% across all the wavelengths studied. PLASMONIC SOLAR CELLS WITH NON-PERIODIC PATTERNS Figure 4 Comparison of simulated generation rate to measured EQE spectrum for Asahi texture. Randomly textured films can be simulated directly in FDTD using imported AFM data. In the case of the Asahi texture shown in Figure 2, the profile of an Ag-coated Asahi substrate was used to directly simulate the performance of a solar cell grown on this type of texture. Rather than making assumptions about conformal broadening from each layer deposition, the same surface profile was propagated through each layer. The AFM scan was measured over a 10 µm x 10 µm region, but given the restrictions on grid sizes necessary for accurate simulation, a smaller subset of 2 µm x 2 µm was used in the simulation, as illustrated in Figure 3. Figure 4 shows a comparison of a-si:h solar cells made on Ag-coated Asahi substrates, compared to the calculated generation rate from simulation. The agreement in shape is good, particularly on the red side of the spectrum. The error on the blue side of the spectrum is slightly more significant, but there are several reasons why this will show slightly more deviation. The measurement in this region will have more error since both the photocurrent from the cell and the lamp power are weak. The assumption of texture propagation without conformal broadening will lead to more error on the blue side of the spectrum, since the blue side photocurrent absorption There are many variables that can be tuned in nanostructure design for enhanced absorption, including the shape and arrangement of nanostructures. We have shown previously that periodic patterns of hemispherical Ag particles can lead to enhanced photocurrent over Asahi textures, but that the effect is dependent on the pitch of the particles: lattices with 500 nm pitch show approximately 10% improvement over Asahi cells, while a lattice with 700 nm pitch is below the photocurrent of the Asahi reference. The periodic cells have particular wavelengths where the absorption is strongly enhanced due to the waveguide modes present at that pitch. Randomly textured surfaces, in contrast, show a smooth EQE spectrum. The arrangement of nanoparticles on the back contact can be engineered in other types of largearea nanopatterns to engineer a broadband response. Quasicrystal tilings represent an intermediate case between periodic, square lattices and a random texture. Here we use a penrose tiling of nanoparticles, which lacks translational symmetry but has both short and long range order [16]. Since this pattern is non-periodic, simulations must be done over a larger computational volume than a periodic square lattice. The simulation results shown here demonstrate both the importance of accounting for conformal depositions in simulation, and a general method for the exploration of complex, quasi-periodic plasmonic nanopatterns. From an experimental standpoint, the measurements here show that quasicrystal nanopatterns are an interesting direction for light trapping design. Solar Cell Fabrication One of the challenges to plasmonic photovoltaics is the fabrication of large-area, controlled nanopatterns that are also scalable and economically feasible. Nanoimprint lithography meets these criteria as a high-throughput method for replication of nanostructures, and the process /11/$ IEEE

4 described here (Substrate Conformal Imprint Lithography) is printable over wafer scale areas with minimal defects, and both the stamps and master wafers are reusable thousands of times [17-19]. We used electron-beam lithography to pattern a Si wafer with a penrose pattern of nanopillars. The pattern was designed over a 100 µm x 100 µm region, and tiled into a 6 mm x 6 mm area. A composite PDMS stamp was molded from this wafer, and embossed into a silica sol-gel resist on glass. After curing, the sol-gel is 88% silica by weight, and stable up to 450 C [18]. The silica patterns were overcoated with Ag by sputtering, then again with ZnO:Al. An n-i-p a-si:h solar cell was grown over the ZnO:Al, and a 4 mm x 4 mm top contact of ITO deposited by sputtering through a shadow mask. The nanopatterns were characterized before deposition using AFM and SEM, and the profile of the solar cells after deposition were confirmed via both SEM cross sections and AFM of the top surface. EQE spectra were measured using a Xenon lamp with one sun light bias applied. Simulation and Results Figure 5 Left: AFM scan of Ag-coated particles as used in fabrication of the solar cell. Right: simulation approximation of nanoparticles surface. Figure 5 shows an experimental AFM measurement of the penrose pattern after overcoating with Ag. The particles closely resemble hemispheres even after coating, and were designed to be 100 nm tall. While this surface could be used as is in simulation, for computational ease we replaced each scatterer with a hemiellipsoid of the same height and diameter, as shown in the right side of Figure 5. This both reduces the complexity of the simulation and allows us to construct a conformally broadened simulation by increasing the diameter and height of each hemiellipsoid with each additional layer included. The fabricated cells were designed to be ultrathin, so the intrinsic regions were 90 nm thick. In ultrathin geometries, broadband light trapping is more important since a smaller percentage of the solar spectrum will be absorbed in a single pass. Plasmonic nanostructures which couple free space sunlight to localized and guided wave modes are thus particularly well-suited to ultrathin devices. Figure 6 Experimental EQE vs. simulated optical generation rate for a-si:h solar cells made over penrose patterns. Figure 6 shows the experimental EQE spectrum of the cell fabricated over the penrose pattern. Notably, the EQE spectrum exhibits a few features, but is relatively broad. This indicates that the penrose pattern is an intermediate case between randomly textured surfaces and strictly periodic light trapping arrays. The patterns were generated so that the minimum spacing between features is 400 nm, but this could be varied to a variety of other pitches to find an optimal design. The result shown here has a 45% higher short circuit current density than a flat reference cell, 30% higher than an Asahi texture reference cell, and 9% higher than our previously used periodic nanopatterns with 500 nm pitch. Again, while the patterns are non-periodic, a 2 µm x 2 µm subsection of the nanopattern was used in simulation, with periodic boundary conditions. The particles were translated and broadened in each layer according to estimates from SEM cross sections. For a 300 nm diameter Ag particle, the diameter of the final ITO particle is approximately 400 nm, making a 400 nm separation between scatterers the minimum separation without overlap of any of the features. The simulation of the penrose-patterned cell agrees very closely with the experimental measurement, and illustrates the importance of using simulation approximations that are similar to the real deposition conditions: by including the conformal deposition of each layer, the calculated blue side of the spectrum is now in close agreement with the measured values. The peaks in the spectrum are reproduced well, if slightly more pronounced since the simulation method accounts only for optical absorption and not carrier collection. In particular the peak around 630 nm is more exaggerated in the simulation, which may be due to incomplete carrier collection in the device /11/$ IEEE

5 (bottom left), indicating that the top-side conformal structure plays an important role in enhancing absorption. CONCLUSIONS Ultrathin film a-si:h solar cells hold several advantages over their thicker counterparts, including reduced materials cost and increased throughput rates and improved stability. Light trapping from plasmonic and other nanophotonic designed systems is one route to achieving enhanced absorption in thin and ultrathin photovoltaics. In the back-contact plasmonic nanostructure design discussed here, incident sunlight couples into both localized and guided modes of the semiconductor to increase absorption. Figure 7 Cross section maps of the photon flux at λ = 630 nm in various permutations of the real structure (top left). CONFORMAL MODELING We can also use simulation to study the importance of texturing the top and back interfaces of the solar cell. Figure 7 shows a cross section map of the photon flux in a few different permutations on the same structure shown in the schematic in Figure 1. The nanostructures are all separated by 500 nm, and these images are at a single wavelength, λ = 630 nm, which is on a waveguide mode resonance of the full structure. The image in the top left is the structure closest to the realistic device, where the Ag nanoparticles are patterned and each successive layer conformally broadens over the underlying pattern. The other three designs do not correspond to experimental devices but allow for a comparison of the absorption from different components: on the top right, a non-plasmonic version of the same cell without Ag nanostructuring, on the bottom left a nonplasmonic cell with structuring only on the top a-si:h and ITO layers, and on the bottom right a plasmonic cell where only the back Ag and ZnO:Al are patterned. In the plasmonic case in the top left, the absorption is particularly high in the local region in the a-si:h over the Ag particle: this is noticeably different in the case on the top right without the Ag particle. For the bottom row, it is clear that the waveguide mode resonances are extremely different from the models that include both front and back-side patterning. The overall absorption is also strongest in the cell with all interfaces textured, indicating that these designs are more effective than texturing either the top or the bottom exclusively. All of the patterns which include top-side texturing show localized modes, while the back-side-only pattern shows only waveguide modes. This is particularly clear in the cell with a textured top and a flat back reflector For any type of nanophotonic design for photovoltaics, electromagnetic simulation can be a useful tool for both optimizing and understanding the optical absorption. We showed here that it is important to include the effects of realistic cell deposition on the geometry to achieve an accurate model of the experimental device. We showed that it is possible to simulate non-periodic structures, such as randomly textured surfaces and quasicrystal tilings, with close correspondence to experimental measurements while being computationally tractable. We also showed that a quasicrystal nanopattern, consisting of a penrose arrangement of nanostructures, is a potential pattern for light trapping in these solar cells which is neither random nor periodic. Finally, by comparing several different permutations on light trapping structures, we showed that nanostructures on all of the interfaces of the solar cell lead to more effective light trapping than any of the layers alone. ACKNOWLEDGEMENTS We are grateful to Karine van der Werf is for solar cell depositions, and to MiPlaza for electron-beam fabrication of the master pattern. The Caltech portion of this work was supported by the Department of Energy under contract number DE-FG02-07ER46405 (modeling) and SETP GO (cell fabrication). Work at AMOLF is part of the research program of FOM which is financially supported by NWO. This work is also part of the Global Climate and Energy Project (GCEP). REFERENCES [1] U. Dagkaldiran, A. Gordijn, F. Finger, H. M. Yates, P. Evans, D. W. Sheel, Z. Remes, M. Vanecek. Amorphous silicon solar cells made with SnO2:F TCO films deposited by atmospheric pressure CVD, Mater. Sci. Eng. B, (Sp. Iss. SI), 2009, pp [2] J. Krc, F. Smole, M. Topic. Potential of light trapping in microcrystalline silicon solar cells with textured substrates, Prog. Photovoltaics, 11, 2003, pp /11/$ IEEE

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